Friction is often the trickiest part of Newton's Laws problems. Understanding its behavior is crucial.

Static vs Kinetic:

• Static friction acts when surfaces are at rest relative to each other
• It is self-adjusting: f_s = applied force (up to mu_s*N)
• At the verge of motion, f_s = mu_s*N (maximum)
• Once motion begins, friction drops to f_k = mu_k*N
• mu_k < mu_s always

Direction of Friction:

• Opposes RELATIVE motion (kinetic) or TENDENCY of relative motion (static)
• Friction on a walking person's foot is FORWARD
• Friction on a box in an accelerating truck is FORWARD
• Friction is not always opposite to the direction of motion

Angle of Repose:

• The maximum angle at which a block remains stationary on a rough incline
• tan(alpha) = mu_s
• For theta > alpha: block slides
• For theta < alpha: block is stationary with f = mgsin(theta) < mu_sN
• For theta = alpha: block is on the verge of sliding

Optimal Pulling Angle:

• To move a block on a rough surface with minimum force, pull at angle lambda = arctan(mu_s) above horizontal
• This minimizes the normal force and therefore friction
• F_min = mg*mu_s/sqrt(1 + mu_s^2)